板梁组合结构有限元分析的未确知因子法

为了克服随机方法对于小样本难以处理的缺陷.文中充分利用客观的不确定性信息,构建了物理参数和载荷同时具有未确知性的空间板梁组合结构有限元分析模型,并提出了基于未确知因子法的板梁组合结构分析方法;利用未确知因子的数学表述和未确知有理数的运算规则,推导出板梁组合结构位移响应和单元应力响应的计算表达式.得出结构位移和应力响应取某值的可信度与各参数取值可信度的趋势是一致的结论.在缺乏足够数据或者信息不完整的情况下,用未确知信息表述结构模型参数的不确定性,比用成熟的随机方法具有更高的可信度且方法简易可行.算例给出了未确知性结构的响应可能值及其可信度的计算结果.表明该方法的可行性和有效性.

Undetermined Factor Method for Finite Element Analysis of Undetermined Beam-plate Composite Structures

Probabilistic method can not be properly applied in case of small sample.To deal with such situations, the undetermined but objective information is considered, and in the finite element analysis model of space beam and plate structures the structural physical parameters and the applied loads are defined as undetermined variables.And a structure analysis method based on the undetermined factor method is proposed.From the expression of undetermined factors, the computational expressions of the structural displacement response and the element stress response are obtained.It is concluded that the confidence levels of structural responses are in direct proportion to the confidence level of each parameter.Compared to the probabilistic method, the proposed method can obtain reliable results with higher confidence levels in case of inadequate number of data or insufficient information;moreover, it is simple and easy to apply.At last, an example is given, in which the possible values and confidence levels of the undetermined structure responses are obtained.The rationality and validity of the presented method are demonstrated.